A freestyle skier hits the take off ramp with an initial velocity of 17.5 m/s with a purely vertical take off (90 degrees). What is the peak height that the skier will reach?
Can you fully explain to me how to get this answer?
I did the formula d=Vi*deltT+(1/2)(a)(t^2). To get time did 17.5m/s/9.81m/s=1.78s. Got the answer 46.69 but the answer is 15.56. I got 15.56 on one side of my equation so idk what I'm doing wrong.
You are using formulas without thinking.
at the peak height, the velocity is zero.
Vf=vi+at
0=17.5 + 9.8t
t= 1.78sec
hfinal=vi*time+1/2 g t^2
= 17.5*1.78-4.9(1.78^2)=15.6m
To find the peak height that the skier will reach, you need to consider the motion of the skier after taking off from the ramp. Since the takeoff is purely vertical, only the vertical component of the initial velocity is relevant for calculating the height.
First, let's find the time it takes for the skier to reach the peak height. You correctly divided the initial velocity (17.5 m/s) by the acceleration due to gravity (9.81 m/s^2) to get the time of 1.78 seconds. This is the time it takes for the skier to reach the highest point of their trajectory.
Now, we can use this time to find the peak height using the equation:
h = Vi * t - (1/2) * g * t^2
Where:
h = peak height
Vi = initial vertical velocity
t = time
g = acceleration due to gravity
In this case, the initial vertical velocity is equal to the initial velocity (17.5 m/s) because the takeoff is purely vertical.
Plugging in the values:
h = 17.5 m/s * 1.78 s - (1/2) * 9.81 m/s^2 * (1.78 s)^2
Calculating this equation will give you the correct peak height.